Projectile Motion Calculator

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Example

Created on 2024-06-20Asked by William Taylor (Solvelet student)

A projectile is launched with an initial velocity of

v_0 = 30

m/s at an angle of

\theta = 45^\circ

with respect to the horizontal. Find the maximum height reached by the projectile.

Solution

To find the maximum height reached by the projectile: 1. Resolve the initial velocity into horizontal and vertical components:

v_{0x} = v_0 \cos \theta, \quad v_{0y} = v_0 \sin \theta.

2. Determine the time taken to reach maximum height using the vertical component:

v_{0y} = gt \implies t = \frac{v_{0y}}{g},

where

g = 9.8

m/s

^2

is the acceleration due to gravity. 3. Calculate the maximum height using the time obtained:

h = v_{0y} t - \frac{1}{2} g t^2.

4. Substitute the values: \[ \begin{aligned} h &= (30 \sin 45^\circ) \left( \frac{30 \sin 45^\circ}{9.8} \right) - \frac{1}{2} \cdot 9.8 \left( \frac{30 \sin 45^\circ}{9.8} \right)^2 \\ &= 15 \left( \frac{30 \sin 45^\circ}{9.8} \right) - \frac{1}{2} \cdot 9.8 \left( \frac{30 \sin 45^\circ}{9.8} \right)^2 \\ &= \frac{15^2}{9.8} - \frac{1}{2} \cdot \frac{15^2}{9.8} \\ &= \frac{225}{9.8} - \frac{1}{2} \cdot \frac{225}{9.8} \\ &= \Solved on Solvelet with Basic AI Model

Some of the related questions asked by Ethan Rivera on Solvelet

1. Calculate the maximum height reached by a projectile launched with an initial velocity of 20 m/s at an angle of 30 degrees.2. Determine the range of a projectile launched with an initial velocity of

15

m/s at an angle of

45

degrees.

DefinitionProjecting the motion of such volitional objects as balls involves the understanding that the only thing that affects them is gravity combined with air resistance and initial velocity in the air. The motion of the object on a curved path, or a parabola, should be discussed as a combination of horizontal and vertical components of motion. Illustration: An even, horizontal toss of the ball off the cliff leads to the combination of projectile motion when there is constant velocity in the horizontal axis of motion and velocity under acceleration in the vertical axis of motion.

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